.^64 



NA TURE 



[August 17, 1893 



common. That M. Vioot should commence his book 

 with references to the Deluge, the destruction of Sodom 

 and Gomorrahj and the giving of the law on Sinai, seems 

 perfectly natural. But most readers will note with some 

 surprise that the last chapter of Dr. Hoernes's book is one 

 entitled " Die Sintfluth." We cannot but regard it as a 

 remarkable testimony to the profound influence of that 

 striking and suggestive book of Dr. Suess, " Das Antlitz 

 der Erde," that this chapter should have been added by 

 Dr. Hoernes to his systematic treatise on Earthquakes. 

 It is scarcely necessary to point out that the flood to 

 which the Austrian geologist devotes the final chapter of 

 his treatise is the deluge, not of Sir Henry Howorth, but 

 of Noah and Hasts-Adra, and that the connexion between 

 this final chapter and the preceding ones is of the very 

 slenderest character. But the legends of our own child- 

 hood and of the childhood of our race have a fascination 

 for us, which neither the brilliant French essayist nor the 

 painstaking German professor seem to have been able to 

 resist. 



067? BOOK SHELF. 



The Points of the Horse. By M. Horace Hayes, 



F.R.C.V.S. (London : W. Thacker and Co., 1893.) 

 It is certainly curious that although the English nation 

 justly prides itself on its knowledge of horse flesh, and 

 its success in producing the various equine breeds, it 

 should possess no work dealing in an exact and scientific 

 manner with the conformation of the animal that it has 

 done so much to improve. That certain shapes are in- 

 dicative of great speed, whilst others point to strength 

 rather than speed, has, of course, always been insisted 

 upon in a general way, but it has been left to Captain 

 Hayes to imitate the example of several French authors, 

 and deal with the subject in a scientific spirit. A soldier, 

 a certificated veterinarian, a traveller, and a successful 

 riier, the author is well qualified to treat of all that per- 

 tains to the subject before us. The work represents a 

 painstaking endeavour to discover and explain the 

 various principles which govern the make and shape of 

 the horse. 



Starting with a study of animals like the Indian black 

 buck and cheetah, which possess terrific speed, he 

 compares them with others such as the buffalo and 

 rhinoceros, which are examples of great strength, a com- 

 parison which leads to the conclusion that animals of 

 great strength are distinguished by a long body and short 

 legs ; those of great speed by a short body and long 

 legs. This is an exemplification of Marey's law that 

 muscles of speed are long and slender, and those of 

 strength short and thick. Whether it was necessary to 

 stray so far from home to find examples of this fact may 

 be doubted. The thoroughbred racehorse on the one 

 hand, and the massive carthorse on the other, are surely 

 sufficiently contrasted types of speed and strength, 

 whilst between the two extremes are numerous examples 

 exhibiting the union of these two attributes in various 

 degrees, the hunter, for example, uniting considerable 

 strength with moderate speed. 



The defects as well as many of the beauties of conforma- 

 tion are admirably depicted in a series of photographs, such 

 defects as turned-in and turned-out toes, sickle-shaped 

 hocks, and upright pasterns, being particularly good. The 

 p'lotographic plates, of which there are over seventy, 

 certainly constitute an important feature in the work, 

 enbracing, in addition to the above, portraits of many 

 celebrated racers, notably " Ormonde " and " St. Simon," 

 as well as horses and ponies of various breeds found in 



NO. 1242, VOL. 48] 



different parts of the globe. A chapter is devoted to an 

 examination of these photographs, the leading features 

 and points of the animals represented being analysed and 

 commented upon. It would be unfair in this connection 

 to omit favourable mention of the 200 excellent drawings 

 by the late J. H. Oswald Brown, which serve throughout 

 the work to illustrate the letterpress. 



Author, artist, and publisher have successfully united 

 in producing a first-rate work, which may be cordially 

 recommended to all lovers— and their name is legion — of 

 the horse. W. F. G. 



LETTERS TO THE EDITOR. 



[ Tht Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part op NATtJRE. 

 No notice is taken of anonymous communications.^ 



Quaternions and Vector Analysis. 



In a paper by Prof. C. G. Knott on "Recent Innova- 

 tions in Vector Theory," of which an abstract has b;en given 

 in Nature (vol. xlvii. pp. 590-593; see alsj a minor a'stract 

 on p. 2S7), the do.;trine that the quaternion affords the only 

 sufficient and proper basis for vector analysis is miintaine i by 

 arguments based so largely on the faults and deficiencies which 

 the author has found in my pamphlet, " EL'ments of Vector 

 Analysis," as to give to such faults an importance which they 

 would not otherwise possess, and to make some reply from me 

 necessary, if I would not discredit the cau5e of non-qua'erni >nic 

 vector analysis. Especially is this true in view of the wirm 

 commendation and endorsement of the paper, by Prof. Tait, 

 which appeared in Nature somewhat earlier (p. 225) 



The charge which most requires a reply is expressed most 

 distinctly in the minor abstract, viz, "that in the develop- 

 ment of his dyadic notation, Prof. Gibbs, being forced to 

 bring the quaternion in, logically condemned his own po5ition." 

 This was incomprehensible to me until I received the original 

 paper, where I found the charge specified as follows : "Although 

 Gibbs gets over a good deal of ground without the explicit 

 recognition of the complete product, which is the difference of 

 his 'skew' and 'direct' products, yet even he recognises in 

 plain language the versorial character of a vector, brings in 

 the quaternion whose vector is the difference of a linear vector 

 function and its conjugate, and does not hesitate to use the 

 accursed thing itself in certain line, surface, and volume 

 integrals" (Proc. R.S.E., Session 1892-3, p. 236). These 

 three specifications I shall consider in their inverse order, pre- 

 mising, however, that the epitheta ornantia are entirely my 

 critic's. 



The last charge is due entirely to an inadvertence. Tlie 

 integrals referred to are those given at the close of the maj ir 

 abstract in Nature (p. 593). My critic, in his original paper, 

 states quite correctly that, according to my definitions and 

 notations, they should represent dyadics. He multiplies them 

 into a vector, introducing the vector under the integral sign, as 

 is perfectly proper, provided, of course, that the vector is 

 constant. But failing to observe this restriction, evidently 

 through ina Ivertence, and finding that the resulting eq'ialions 

 (thus interpreted) would not be true, he concludes that I must 

 have meant something else by the original equations. Now, 

 these equations will hold if interpreted in the quaternionic 

 sense, as is, indeed, a necessary consequence of their holding 

 in the dyadic sense, although the converse would not be true. 

 My critic was thus led, in consequence of the inadvertence 

 mentioned, to suppose that I had departed from my ordinary 

 usage and my express definitions, and had intended the pro- 

 ducts in these integrals to be tal<en in the quaternionic sense. 

 This is the sole ground for the last charge. 



The second charge evidently relates to the notations *s and 

 **x (see Nature, vol. xlvii. p. 592). It is perfectly true that I 

 have used a scalar and a vector connected with the linear vector 

 operator, which, if combined, would form a quaternion. I have 

 not thus combined them. Perhaps Prof. Knott will say that since 

 I use both of them it matters little whether I cojibine them or 

 not. If so I heartily agree with him. 



The first charge is a little vague. I certainly admit that 



